Thermal neutron cross-section and resonance integral of the Mo(n,γ)Mo reaction

We measured the thermal neutron cross-section and the resonance integral of the ⁹⁸Mo(n,γ)⁹⁹ Mo reaction by the activation method using a ¹⁹⁷Au(n,γ)¹⁹⁸ Au monitor reaction as a single comparator. The high-purity natural Mo and Au metallic foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility. The induced activities in the activated foils were measured with a calibrated p-type high-purity Ge detector. The necessary correction factors for the γ-ray attenuation (F_g), the thermal neutron self-shielding (G_th) and the resonance neutron self-shielding (G_epi) effects, and the epithermal neutron spectrum shape factor (α) were taken into account. In addition, for the ⁹⁹Mo activity measurements, the correction for true coincidence summing effects was also taken into account. The thermal neutron cross-section for the ⁹⁸Mo(n,γ)⁹⁹Mo reaction has been determined to be 0.136 ± 0.007 barn, relative to the reference value of 98.65 ± 0.09 barn for the ¹⁹⁷Au(n,γ)¹⁹⁸ Au reaction. The present result is, in general, in good agreement with most of the experimental data and the recently evaluated values of ENDF/B-VII.0, JENDL-3.3, and JEF-2.2 by 5.1% (1σ). By assuming the cadmium cut-off energy of 0.55 eV, the resonance integral for the ⁹⁸Mo(n,γ)⁹⁹Mo reaction is 7.02 ± 0.62 barn, which is determined relative to the reference values of 1550 ± 28 barn for the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction. The present resonance integral value is in general good agreement with the previously reported data by 8.8% (1σ).     

An analytical multigroup benchmark for (n, γ) and (n, n′, γ) verification of diffusion theory algorithms

The angular flux for the “rod model” describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.     

Measurement of neutron capture cross-section of the Ga(n, γ)Ga reaction at 0.0536 eV energy

The neutron capture cross-section for the ⁷¹Ga(n,  γ)⁷²Ga reaction at 0.0536 eV energy was measured using activation technique based on TRIGA Mark-II research reactor. The ¹⁹⁷Au(n, γ)¹⁹⁸Au monitor reaction was used to determine the effective neutron flux. Neutron absorption and γ-ray attenuation in gallium oxide pellet were corrected in determination of cross-section. The cross-section for the above reaction at 0.0536 eV amounts to 2.75 ± 0.14 b. As far as we know there are no experimental data available at our investigated energy. So far we are the first, who carried out experiment with 0.0536 eV neutrons for cross-section measurement. The present result is larger than that of JENDL-3.3, but consistent within the uncertainty range. The value of ENDF/B-VII is higher than this work. The result of this work will be useful to observe energy dependence of neutron capture cross-sections.     

Measurement of thermal neutron cross-section and resonance integral for the Ho(n,γ)Ho reaction using electron linac-based neutron source

The thermal neutron cross-section and the resonance integral of the ¹⁶⁵Ho(n,γ)^166gHo reaction have been measured by the activation method using a ¹⁹⁷Au(n,γ)¹⁹⁸Au monitor reaction as a single comparator. The high-purity natural Ho and Au foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility. The induced activities in the activated foils were measured with a calibrated p-type high-purity Ge detector. The correction factors for the γ-ray attenuation (F_g), the thermal neutron self-shielding (G_th), the resonance neutron self-shielding (G_epi) effects, and the epithermal neutron spectrum shape factor (α) were taken into account. The thermal neutron cross-section for the ¹⁶⁵Ho(n,γ)^166gHo reaction has been determined to be 59.7 ± 2.5 barn, relative to the reference value of 98.65 ± 0.09 barn for the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction. By assuming the cadmium cut-off energy of 0.55 eV, the resonance integral for the ¹⁶⁵Ho(n,γ)^166gHo reaction is 671 ± 47 barn, which is determined relative to the reference value of 1550 ± 28 barn for the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction. The present results are, in general, good agreement with most of the previously reported data within uncertainty limits.     

Measurement of thermal neutron cross-section and resonance integral for the Yb(n,γ)Yb reaction by the cadmium ratio method

The thermal-neutron cross-section and the resonance integral for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction were measured by the activation method using a ⁵⁵Mn monitor as single comparator. Analytical grade MnO₂ and Yb₂O₃ powder samples with and without a cylindrical 1 mm Cd shield box were irradiated in an isotropic neutron field obtained from three ²⁴¹Am-Be neutron sources. The gamma-ray spectra from the activated samples were measured with a calibrated n-type high-purity Ge detector. The experimental results were corrected for the correction factors calculated for thermal and epithermal neutron self-shielding effects, epithermal neutron spectrum shape and gamma-ray self attenuation. Thus, the thermal neutron cross-section for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction is found to be 126.5 ± 6.6 b, relative to that of the ⁵⁵Mn monitor. The resonance integral value for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction is found to be 59.6 ± 8.5 b, at cadmium cut-off energy of a 0.55 eV. Using the measured cadmium ratios of ⁵⁵Mn and ¹⁷⁴Yb, the result for resonance integral of the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction has also been obtained relative to the reference value of the ⁵⁵Mn monitor. The present results for the ¹⁷⁴Yb(n,γ)¹⁷⁵Yb reaction agree well only with the recent experimental ones obtained by Kafala et al. [1] and De Corte and Simonits [2] within uncertainty limits. However, the previously reported experimental data for the thermal neutron cross-section for this reaction are distributed between 24 and 141 b, and similarly the experimental values for the resonance integral value also show a large scatter in the range of 30-69 b.     

Measurement of thermal neutron cross-section and resonance integral for 186W(n,γ)187W reaction by the activation method using a single monitor

The thermal neutron cross-section (σ₀) and the resonance integral (I₀) of the reaction ¹⁸⁶W(n,γ)¹⁸⁷W were measured by the activation method using ⁵⁵Mn as a single comparator. The diluted MnO₂ and WO₃ samples within and without a cylindrical Cd shield case were irradiated in an isotropic neutron field of the ²⁴¹Am–Be neutron source. The γ-ray spectra from the irradiated samples were measured by high resolution γ-ray spectrometry with a calibrated high purity Ge detector. The necessary correction factors for gamma ray attenuation, thermal and resonance neutron self-shielding effects, and the shape factor (α) for epithermal neutron spectrum were taken into account in the determinations. The thermal neutron cross-section for ¹⁸⁶W(n,γ)¹⁸⁷W reaction has been determined to be 39.5±2.3 b at 0.025 eV. This result has been obtained relative to the reference thermal neutron cross-section value of 13.3±0.1 b for the ⁵⁵Mn(n,γ)⁵⁶Mn reaction. The present value of 39.5±2.3 b for ¹⁸⁶W(n,γ)¹⁸⁷W, in general is in good agreement with most of experimental data and evaluated ones in ENDF/B-VI and JENDL-3.2 within the limits of error. The resonance integral has also been measured relative to the reference value of 14.0±0.3 b for the ⁵⁵Mn(n,γ)⁵⁶Mn monitor reaction using a 1/E^1+α epithermal neutron spectrum of the ²⁴¹Am–Be neutron source. By defining Cd cut-off energy 0.55 eV, the resonance integral obtained was 493±40 b. The existing experimental and evaluated data for the resonance integral are distributed from 290 to 534 b. The present resonance integral value agrees with some previously reported values.     

Systematics studies of (n, α) reaction cross sections at 14.5 MeV neutrons energy

A new semi-empirical formula for the calculation of the (n, α) cross-section at 14.5 MeV neutron energy is obtained. It is based on the pre-equilibrium exciton and evaporation models and uses the Droplet model of Myers and Swiatecki to express the reaction energy Q(n, α). The systematics behavior of the different terms of the Droplet model involved in Q(n, α) was checked individually before choosing the pertinent terms and setting up the formula. Fitting this formula to the existing cross-section data, the adjustable parameters have been determined and the systematics of the (n, α) reaction have been studied. The predictions of this formula are compared with those of the existing formulae and with the experimental data. The formula with five parameters is found to give a better fit to the data than the previous comparable formulae.     

Excitation functions of (n, α) reaction cross-sections for some important isotopes from threshold to 20 MeV

The (n, α) reaction cross-sections from threshold to ∼20 MeV on some important nuclides ⁴²Ca, ^50,53Cr, ^56,57Fe, ^58,62Ni, and ^63,65Cu involved in the reactor shielding design have been calculated using the Hauser–Feshbach statistical model with preequilibrium effects by involving PCROSS option in Empire 2.19. The transmission coefficients for neutrons in the entrance channel are calculated using the optical model potential of Koning. In the exit channel optical model potential of Avrigeanu has been used. The experimental values have been chosen carefully for all the isotopes, from EXFOR data base. The calculations are compared with existing experimental data as well as with evaluated data files (ENDF/B-VI.0 and JENDL-3.3). A good agreement between the calculated and experimental data validates the nuclear model approaches with increased predictive power to supplement and extend the nuclear database that is required for several applications.     

Measurement of cross sections for (n, 2n), (n, p) and (n, α) reactions on germanium isotopes induced by 14 MeV neutrons

Activation cross sections at the neutron energy about 14 MeV on germanium isotopes have been measured, employing the activation technique and γ-ray spectrometry. The data of the cross section are reported for the (n, 2n), (n, p) and (n, α) reactions. The neutron flux was determined using the monitor reactions ²⁷Al (n, α) ²⁴Na and the neutron energies were measured by the method of cross section ratios for ⁹⁰Zr (n, 2n) ⁸⁹Zr to ⁹³Nb (n, 2n) ^92mNb reactions. The measured results were compared with the other measurements.     

Measurements of the Y(n,γ)Y cross-section in the neutron energy range of 13.5-14.6 MeV

The ⁸⁹Y(n,γ)^90mY cross-section has been measured at three neutron energy points between 13.5 and 14.6 MeV using the activation technique and a coaxial HPGe γ-ray detector. The data for the ⁸⁹Y(n,γ)^90mY cross-sections are reported to be 0.39 ± 0.02, 0.43 ± 0.02, and 0.38 ± 0.02 mb at 13.5 ± 0.2, 14.1 ± 0.1, and 14.6 ± 0.2 MeV incident neutron energies, respectively. The first data for the ⁸⁹Y(n,γ)^90mY reaction at neutron energy points of 13.5 and 14.1 MeV are presented. The natural high-purity Y₂O₃ powder was used as target material. The fast neutrons were produced by the T(d,n)⁴He reaction. Neutron energies were determined by the method of making cross-section ratios of ⁹⁰Zr(n,2n)^89m+gZr and ⁹³Nb(n,2n)^92mNb reactions, and the neutron fluencies were determined using the monitor reaction ⁹³Nb(n,2n)^92mNb. The results obtained are compared with existing data.     

Calculation and analysis of n+Zr reactions in the En ⩽ 250 MeV energy range

All of reaction cross sections, angular distributions, energy spectra, γ-ray production cross sections, and the double differential cross section for neutron, proton, deuteron, triton, helium and alpha emission are calculated and analyzed for n+^{90,91,92,94,96,nat}Zr at incident neutron energies from 0.1 to 250 MeV. The optical model, intranuclear cascade model, the unified Hauser–Feshbach theory and the exciton model which included the improved Iwamoto–Harada model are used. Theoretical calculated results are compared with existing experimental data and other evaluated data from ENDF/B-VI.8, ENDF/B-VII.0 and JENDL-3.3. The optical model potential parameters are obtained according to the experimental data of total, nonelastic cross sections and elastic scattering angular distributions.     

Measurement of thermal neutron and resonance integral cross sections of the reaction V(n,γ)V using a 20 Ci Am–Be isotopic neutron source

The thermal neutron capture cross section (σ_o) and the resonance integral (I_o) of the ⁵¹V(n,γ)⁵²V reaction were measured with an activation method to provide fundamental data for reactor calculation, activation analysis, and other theoretical and experimental uses concerning the interaction of neutron with matter. The vanadium and manganese samples were irradiated within and without a Cd shield case using a 20 Ci Am–Be neutron source. The activities of the samples were measured using gamma-ray spectroscopy. The thermal neutron capture cross section and the resonance integral were determined relative to the reference reaction ⁵⁵Mn(n,γ)⁵⁶Mn and the values obtained are 5.16 ± 0.19 barns and 2.53 ± 0.1 barns respectively. The previous measurements of the σ_o and I_o of the reaction ⁵¹V(n,γ)⁵²V were reviewed and the difference between the present values and the previous results were discussed.     

Depth profiling of Mg by 2010 keV resonance of Mg(p,p′γ)Mg nuclear reaction

Studies on the characteristics of 2010 keV resonance in ²⁴Mg(p,p′γ)²⁴Mg nuclear reaction for depth profiling Mg in thin films are reported. The resonance reaction, based on the detection of characteristic 1368 keV γ-rays, enables interference free measurement of Mg down to 2 × 10²⁰ atoms/cm³ and has a probing depth of about 20 μm. The width of the resonance extracted from excitation curves for thick (>180 nm) thermally grown elemental Mg films, by SPACES is about 350 ± 50 eV. The reaction has been used to depth profile Mg in a Mg/Ti/Mg/Si film which provides interesting information on interfacial mixing involving Ti layer and the underlying Mg layer.     

Thermal neutron capture cross sections for the Sm(n,γ)Sm and Sm(n,γ)Sm reactions at 0.0536 eV energy

The neutron capture cross sections for the ¹⁵²Sm(n,γ)¹⁵³Sm and ¹⁵⁴Sm(n,γ)¹⁵⁵Sm reactions at 0.0536 eV neutron energy were measured using an activation technique based on the TRIGA Mark-II research reactor, relative to the reference reaction ¹⁹⁷Au(n,γ)¹⁹⁸Au. The activity was measured nondestructively using gamma-ray spectroscopy. Our measured values at this neutron energy are the first ones and are compared with 1/v based evaluated cross sections reported in the ENDF/B-VII and JENDL-3.3 libraries. The measured value for the ¹⁵²Sm(n,γ)¹⁵³Sm reaction is 0.28% lower than JENDL-3.3 and 0.48% higher than ENDF/B-VII. Our value for the production of ¹⁵⁵Sm is about 3% and 2.3% higher than the evaluated value with ENDF/B-VII and JENDL-3.3 at 0.0536 eV, respectively.     

Determination of thermal neutron cross-section and resonance integral for the As (n, γ)As reaction by activation method using Mn (n, γ)Mn as a monitor

Nuclear constants for use in reactor activation analysis especially (n, γ) cross-sections and absolute gamma intensities, are known to show a rather large scatter in literature. Thermal and resonance cross-sections for the ⁷⁵As (n, γ)⁷⁶As reaction is determined by the method of foil activation using ⁵⁵Mn (n, γ)⁵⁶Mn as a reference reaction. The experimental sample with and without a cadmium cover of 1-mm wall thickness was irradiated in the isotropic neutron field of the outer irradiation sites 7 of Ghana Research Reactor-1 facility which is a miniature neutron source reactor designed by the Chinese. The irradiation channel used has a neutron spectral parameter (α) found to be (0.037 ± 0.001). The induced activity in the sample was measured by gamma ray spectrometry with a high purity germanium detector. A standard solution of Arsenic was used for the analysis. The necessary correction for gamma attenuation, thermal neutrons and resonance neutron self-shielding effects were not taken into account during the experimental analysis because they were negligible. By defining cadmium cut-off energy of 0.55 eV, the result for ⁷⁵As (n, γ)⁷⁶As reaction was found to be: thermal neutron cross-section σ₀ = (4.28 ± 0.19) b and resonance integral I₀ = (61.88 ± 1.07) b.     

Measurement of thermal neutron capture cross section and resonance integral of the 138Ba(n, γ)139Ba reaction using 55Mn(n, γ)56Mn as a monitor

The thermal neutron capture cross section (σ_o) and the resonance integral cross section (I_o) of the ¹³⁸Ba(n, γ)¹³⁹Ba reaction have been measured by the activation method using the Ghana Research Reactor-1 (GHARR-1). The barium and manganese targets were irradiated within and without a cadmium capsule. The result of the thermal neutron capture cross section for the ¹³⁸Ba(n, γ)¹³⁹Ba reaction is 0.53 ± 0.01barns. The result was obtained relative to the reference value 13.2 barns of the ⁵⁵Mn(n, γ)⁵⁶Mn reaction. The resonance integral cross section for the ¹³⁸Ba(n, γ)¹³⁹Ba reaction was also measured relative to the reference value of 13.9 barns for the ⁵⁵Mn(n, γ)⁵⁶Mn reaction. The present resonance integral cross section for the ¹³⁸Ba(n, γ)¹³⁹Ba reaction is 0.380 ± 0.005 barns. The previous measurements of the σ_o and I_o of the reaction ¹³⁸Ba(n, γ)¹³⁹Ba were reviewed and the difference between the present values and the previous results were discussed. The present work was undertaken with the aim to contribute to the experimental basis of σ_o and I_o evaluations.     

Measurement of thermal neutron cross-sections and resonance integrals for Hf(n,γ)Hf and Hf(n,γ)Hf reactions at the Pohang neutron facility

The thermal-neutron cross-sections and the resonance integrals for the ¹⁷⁹Hf(n,γ)^180mHf and the ¹⁸⁰Hf(n,γ)¹⁸¹Hf reactions have been measured by the activation method. The high purity Hf and Au metallic foils within and without a Cd shield case were irradiated in a neutron field of the Pohang neutron facility. The gamma-ray spectra from the activated foils were measured with a calibrated p-type high-purity Ge detector.In the experimental procedure, the thermal neutron cross-sections, σ₀, and resonance integrals, I₀, for the ¹⁷⁹Hf(n,γ)^180mHf and the ¹⁸⁰Hf(n,γ)¹⁸¹Hf reactions have been determined relative to the reference values of the ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction, with σ₀ = 98.65 ± 0.09 barn and I₀ = 1550 ± 28 barn. In order to improve the accuracy of the experimental results, the interfering reactions and necessary correction factors were taken into account in the determinations. The obtained thermal neutron cross-sections and resonance integrals were σ₀ = 0.424 ± 0.018 barn and I₀ = 6.35 ± 0.45 barn for the ¹⁷⁹Hf(n,γ)^180mHf reaction, and σ₀ = 12.87 ± 0.52 barn and I₀ = 32.91 ± 2.38 barn for the ¹⁸⁰Hf(n,γ)¹⁸¹Hf reaction. The present results are in good agreement with recent measurements.     

Simulation of e–γ–n targets by FLUKA and measurement of neutron flux at various angles for accelerator based neutron source

A 6 MeV Race track Microtron (an electron accelerator) based pulsed neutron source has been designed specifically for the elemental analysis of short lived activation products where the low neutron flux requirement is desirable. The bremsstrahlung radiation emitted by impinging 6 MeV electron on the e–γ primary target, was made to fall on the γ–n secondary target to produce neutrons. The optimisation of bremsstrahlung and neutron producing target along with their spectra were estimated using FLUKA code. The measurement of neutron flux was carried out by activation of vanadium and the measured fluxes were 1.1878 × 10⁵, 0.9403 × 10⁵, 0.7428 × 10⁵, 0.6274 × 10⁵, 0.5659 × 10⁵, 0.5210 × 10⁵ n/cm²/s at 0°, 30°, 60°, 90°, 115°, 140° respectively. The results indicate that the neutron flux was found to be decreased as increase in the angle and in good agreement with the FLUKA simulation.     

Measurement of differential cross-sections and widths of resonances in S(p,p′γ) S reaction in the 3.0-4.0 MeV region

The paper reports the widths and differential cross-sections of resonances at 3.089, 3.379 and 3.717 MeV in the ³²S(p,p′γ)³²S nuclear reaction. The cross-sections are computed at 0° and 90° angles (relative to the beam direction) from thick target excitation curves constructed by measuring 2230 keV γ-rays, characteristic of the reaction. The differential cross-sections of resonances are about 18, 64 and 70 mb/sr respectively at 0° angle and decrease by about half around an angle of 90°. The first resonance, the sharpest among the three, exhibits a width of about 400 eV while those at 3.379 and 3.717 MeV are in 1.0-1.5 keV range. The widths of the resonances are extracted from the respective thick target excitation curves by an interquartile separation method and also by simulating their leading edges. A study of thick target yields in the 3.0-4.0 MeV proton energy region for several sulphide forming elements shows the absence of any significant interference. These resonances, as a result, can be effectively utilised for sensitive and high resolution depth profile measurements of sulphur in films and materials surfaces.     

Measurements of activation cross sections for Lu(n, α)Tm,Lu(n, α)Tm and Lu(n, p)Yb reactions induced by neutrons around 14 MeV

The cross sections for the ¹⁷⁵Lu(n, α)¹⁷²Tm, ¹⁷⁶Lu(n, α)¹⁷³Tm and ¹⁷⁵Lu(n, p)^175m+gYb reactions have been measured in the neutron energy range of 13.5–14.8 MeV using the activation technique. The first data for ¹⁷⁵Lu(n, α)¹⁷²Tm reaction cross sections are presented. In our experiment, the fast neutrons were produced via the ³H(d, n)⁴He reaction on K-400 Neutron Generator at Chinese Academy of Engineering Physics (CAEP). Induced gamma activities were measured by a high-resolution (1.69 keV at 1332 keV for ⁶⁰Co) gamma-ray spectrometer with high-purity germanium (HPGe) detector. Measurements were corrected for gamma-ray attenuations, random coincidence (pile-up), dead time and fluctuation of neutron flux. The neutron fluences were determined by the cross section of ⁹³Nb(n, 2n)^92mNb or ²⁷Al(n, α)²⁴Na reactions. The neutron energy in the measurement was by the cross section ratios of ⁹⁰Zr(n, 2n)^89m+gZr and ⁹³Nb(n, 2n)^92mNb reactions. The results were discussed and compared with experimental data found in the literature and with results of published empirical formulae.